中文摘要：

考虑同时存在两类不同用户（自私用户和利他用户）的混合均衡交通网络的效率损失.其中,自私用户按照用户均衡原则选择出行路径,利他用户按照最小化自身的理解出行成本选择出行路径,其理解出行成本是自私项和利他项的线性组合.首先,构建了刻画这类混合均衡交通分配的变分不等式模型;然后,运用解析推导的方法得到了这类混合均衡交通分配的效率损失上界,并分析了效率损失上界和参数之间的关系;最后,给出了数值算例.研究结果表明,效率损失上界和系统的最大、最小利他系数及路段出行成本函数相关.数值算例表明解析方法是可行的.

英文摘要：

Existing research mainly focuses on the efficiency loss of homogeneous users in the transportation network while little effort has been made to explore the efficiency loss of heterogeneous users.The aim of this article is to investigate the efficiency loss of mixed traffic assignment in the transportation network with selfish and altruistic users.The selfish user chooses a travel path based on the classical user equilibrium （UE） principle and the altruistic user aims to minimize their perceived travel cost （here,the perceived travel cost of each altruistic user is a linear combination of a selfish and altruistic component）.Firstly,this article establishes a Variational Inequality （VI） model to depict this mixed traffic assignment.Secondly,the upper bound of this mixed equilibrium traffic assignment is derived by analytic derivation and the relation between the upper bound and the network parameters is obtained.Finally,a numerical example is carried out to validate the analytical result.The analytical and numerical results show that the upper bound of efficiency loss is related to the maximal altruism coefficient,the minimal altruism coefficient and the link travel cost functions.